Suraromu

Background

This is a Nikoli original.

Puzzle and Goal

An unsolved puzzle consists of a rectangular grid, some of which are colored black. Some cells contain dotted lines representing gates; some of these gates are numbered to either side. One cell contains an open circle with a number in it.

The goal is to draw a single closed loop that satisfies the clues.

Rules

The solved grid must satisfy the following conditions:

The loop begins and ends at the open numbered circle.

The loop must go through each gate exactly once.

If a gate is numbered, the loop must go through it in the appropriate order (for instance, gate 2 must be the second gate passed through).